1. Field of the Invention
The invention relates to machined micro-mechanisms comprising return elements in the form of beams subjected to simultaneous bending and torsion deformations. More precisely, the invention relates to diapason type gyrometers using a micro-mechanical structure of vibrating beams.
2. Description of the Related Art
In some machined micro-mechanisms, it is sometimes necessary to have resonance modes in translation and other resonance modes in rotation simultaneously. The sensitive element of a diapason gyrometer is one of these micro-mechanisms.
FIG. 1 shows a simplified drawing of a sensitive micro-machined element 10 of a diapason type gyrometer with a symmetrical double beam structure. The sensitive element has two degrees of freedom about the Ox and Oz axes perpendicular to a reference coordinate system Oxyz. The purpose of the gyrometer is to measure the angular velocity xcexa9 of the reference Oxz rotating about the Oy axis perpendicular to this reference.
The sensitive element of the gyrometer comprises a first pair of two excitation beams 12 and 14, and a second pair of two other excitation beams 16 and 18. The excitation beams in the first pair and the second pair are located in the same Oxy plane of the reference coordinate system and are parallel to a sensitive axis YYxe2x80x2 coincident with the Oy axis. The first and the second pairs are located on opposite sides of the YYxe2x80x2 axis and at approximately equal distances from it.
Each pair of excitation beams comprises a central mass connecting the two beams in the pair at their center, a mass ml at the middle of the first pair and a mass m2 at the middle of the second pair.
The ends of the beams 12, 14, 16, 18 located on one side are connected to a first transverse element 20 and to a second transverse element 22 located in the same Oxy plane as the excitation beams and approximately perpendicular to these beams.
The first 20 and second 22 transverse elements comprise a first return beam 24 and a second return beam 26 (or return element) respectively, that have torsion axes collinear with the sensitive axis YYxe2x80x2 of the gyrometer. The ends of the first and the second return beams are connected to a first frame 28 and a second frame 30 respectively, rigidly fixed to the gyrometer.
In order to measure the angular velocity during one rotation of the gyrometer, an electrostatic device 32 creates deliberate excitations E1 and E2 respectively on masses m1 and m2 respectively at the resonant natural frequency of the excitation beams and the return beams. These excitation forces E1 and E2 have the same amplitude but opposite directions, and are applied to masses m1 and m2 parallel to an XXxe2x80x2 axis coincident with the Ox axis of the reference coordinate system. The excitations E1 and E2 produce displacements of masses m1 and m2 in two opposite directions at instantaneous velocities v1 and v2 respectively. One rotation of the gyrometer with a sensitive element 10 subject to excitations E1 and E2 produces a pair of Coriolis forces F1 and F2 about the sensitive axis YYxe2x80x2 on masses m1 and m2 respectively, causing a rotation of the transverse elements 20, 22 and torsion of the return beams 24 and 26 about this axis.
The angular rotation velocity xcexa9 of the sensitive element 10 is determined by a measurement of the position of masses m1 and m2. The Coriolis moment at masses m1 and m2 is calculated as follows:       Mcor    ⁢                  /            y        =            ⅆ              ⅆ        t              ⁢          (              J        ·        Ω            )      
where J≈J0+J1sin xcfx89t
Mcor/y: Coriolis moment applied on masses m1 and m2;
xcexa9: angular velocity of the sensitive element 10 about the sensitive axis YYxe2x80x2;
xcfx89: natural angular frequency of masses m1 and m2;
J: moment of inertia of masses m1 and m2 about the YYxe2x80x2 axis;
Jo: constant part of the moment of inertia J;
J1: oscillating part of the moment of inertia generated by movement of the masses about the XXxe2x80x2 axis at the natural angular frequency xcfx89.
The positions of the masses m1 and m2 are calculated by capacitive effect, and the angular velocity xcexa9 of the gyrometer is calculated using known methods making use of the masses m1 and m2 and the torsion and the bending constants of the beams of the sensitive element.
Coriolis forces exerted on the element during one rotation of the gyrometer create a torsion in the return elements at the oscillation frequency of the excitation, while the deliberate excitation of masses m1 and m2 causes bending of the excitation beams.
The resulting bending force and amplitude of bending on a beam are related to each other by Young""s modulus for the material used, while the torsion forces and the resulting torsion angle for the same material are related by Poisson""s ratio for the mechanical behavior that varies depending on the geometry of the beam subjected to torsion.
In gyrometers according to known practice, an attempt is made to make two systems of beams (excitation beams and detection beams) that have the closest possible resonant natural frequencies to amplify the two movements (the excitation vibration movement and the detection vibration movement) produced by the Coriolis force on the sensitive element 10. On gyrometers according to known practice, the excitation vibration takes place on a bending mode, whereas the detection vibration takes place on a torsion mode.
These two resonance modes have different behaviors in terms of frequency variation
as a function of beam machining uncertainties: the stiffness of a beam with a rectangular cross-section in bending depends mainly on its thickness and length, whereas the stiffness in torsion depends mainly on the thickness and the width. The two types of stiffness are expressed by:
Stiffness in bending: Kbending proportional to E.W.(H3/L3)
Stiffness in torsion: Ktorsion proportional to [E./2(1xe2x88x92xcexd)].W3.H3/[L.(W2+H2)]
where L, W, and H are the length, width and depth of the beams,
E and xcexd are the Young""s modulus and the Poisson""s ratio for the material.
as a function of the temperature: the bending mode being related only to the Young""s modulus for the material, while the torsion is dependent on Young""s modulus and Poisson""s ratio; these two parameters do not have the same thermal behavior and therefore do not vary in the same way to temperature fluctuations applied to the gyrometer.
These disadvantages cause a change in the resonant frequencies between beams operating in different modes (bending and torsion), that limit the performance and stability of the gyrometers.
In order to overcome the disadvantages of angular velocity measurement systems according to prior art, the invention proposes m gyrometer comprising a micro-machined sensitive element with at least two symmetrically positioned excitation beams on each side of and parallel to a sensitive Oy axis of the gyrometer, excited in bending about an Ox axis perpendicular to the sensitive Oy axis, and connected through their ends to at least one transverse element fixed in its central part to the sensitive Oy axis, to a frame through an elastic torsion return element acting in opposition to the rotation of the transverse element about the Oy axis, characterized in that elastic return element(s) are sized such that the variation of their resonant natural frequency in torsion with temperature is similar to the variation of the resonant natural frequency in bending of the beams with temperature.
According to a first embodiment of the gyrometer according to the invention, the elastic return element of a transverse element comprises at least one beam elongated in a direction perpendicular to the Oy axis such that the torsion return force due to this elastic return element is essentially due to the resistance of this elongated beam to bending.
In a second embodiment of the gyrometer according to the invention, the elastic return element comprises two elongated beams approximately parallel to each other and attached to each other at their ends on the same side, the central part of one of the beams being attached to the transverse element and the central part of the other beam being attached to the central part of the frame.
In another embodiment of the gyrometer according to the invention, the elastic return element comprises three approximately parallel elongated beams, a first beam attached through one of its end to the transverse element, a second beam attached through one of its ends to the frame, and a third beam attached through one of its ends to the other end of the first beam and through its other end to the other end of the second beam.
In these embodiments according to the invention, the various return elements are subject to forces that essentially produce deformations in bending and very small deformations in torsion, unlike machined micro-mechanical devices according to prior art (sensitive element 10 in FIG. 1) comprising excitation beams subjected to forces causing deformation by bending and return beams subjected to forces causing deformation by torsion (rotation torque about the YYxe2x80x2 sensitive axis).
During vibrational excitation of excitation beams of the sensitive element 10 in FIG. 1, the resonant frequencies of beams deformed in bending and beams deformed in torsion are expressed differently, and in this case the dimensions of the excitation beams and the return beams will be very different if it is required to make these beams vibrate at the same resonant frequency. The return beam to which torsion forces are applied will be shorter than the excitation beam to which bending forces are applied.
The geometric manufacturing uncertainties affect these two resonance modes very differently (in bending and in torsion) and it is difficult to obtain two superposed resonant frequencies. Furthermore in the sensitive element 10 in FIG. 1, the return beam has a rectangular section instead of a round section, therefore the torsion mode is not pure and consequently is difficult to predict precisely. Finally, the frequencies of the torsion and bending modes do not vary with temperature in the same way, possibly creating thermal instabilities in resonance.
Another disadvantage of the sensitive element 10 in FIG. 1 is the appearance of a shift between resonant natural frequencies of the excitation beams and return beams due to manufacturing dispersions. The same geometric variation in the excitation beams and in the return beams will modify the corresponding natural frequencies in bending and torsion differently.
In the micro-mechanical device according to the invention machined from the same material (normally silicon), the elongated beams are essentially subjected to bending forces and therefore deformations are determined as a function of the Young""s modulus. The attachments of the elongated beams of a return element are composed of beams that are short in the direction of the Oy sensitive axis in order to have good resistance to torsion.